Solve for $x$ and $y$ using elimination. ${2x+5y = 47}$ ${-5x-6y = -72}$
We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the top equation by $6$ and the bottom equation by $5$ ${12x+30y = 282}$ $-25x-30y = -360$ Add the top and bottom equations together. $-13x = -78$ $\dfrac{-13x}{{-13}} = \dfrac{-78}{{-13}}$ ${x = 6}$ Now that you know ${x = 6}$ , plug it back into $\thinspace {2x+5y = 47}\thinspace$ to find $y$ ${2}{(6)}{ + 5y = 47}$ $12+5y = 47$ $12{-12} + 5y = 47{-12}$ $5y = 35$ $\dfrac{5y}{{5}} = \dfrac{35}{{5}}$ ${y = 7}$ You can also plug ${x = 6}$ into $\thinspace {-5x-6y = -72}\thinspace$ and get the same answer for $y$ : ${-5}{(6)}{ - 6y = -72}$ ${y = 7}$